Euclid's Elements of Geometry, Libros 1-6;Libro 11Henry Martyn Taylor The University Press, 1895 - 657 páginas |
Dentro del libro
Resultados 1-5 de 84
Página 25
... bisected at right angles by the diagonal AC . 5. Prove that the triangle , whose vertices are the middle points of the sides of an equilateral triangle , is equilateral . 6. Prove that the triangle , formed by joining the middle points ...
... bisected at right angles by the diagonal AC . 5. Prove that the triangle , whose vertices are the middle points of the sides of an equilateral triangle , is equilateral . 6. Prove that the triangle , formed by joining the middle points ...
Página 27
... bisected by the straight lines BD and CD , DBC will be an isosceles triangle . 2. BAC is a triangle having the angle B double of the angle A. If BD bisect the angle B and meet AC at D , BD is equal to AD . 3. Prove by the method of ...
... bisected by the straight lines BD and CD , DBC will be an isosceles triangle . 2. BAC is a triangle having the angle B double of the angle A. If BD bisect the angle B and meet AC at D , BD is equal to AD . 3. Prove by the method of ...
Página 32
... bisect it . CONSTRUCTION . Take any point D in AB , and from AC cut off AE equal to AD . ( Prop . 3. ) Draw DE , and on DE , on the ... bisected by the straight line AF . In the construction for this proposition it is said that 32 BOOK I.
... bisect it . CONSTRUCTION . Take any point D in AB , and from AC cut off AE equal to AD . ( Prop . 3. ) Draw DE , and on DE , on the ... bisected by the straight line AF . In the construction for this proposition it is said that 32 BOOK I.
Página 33
... bisecting the angle contained by two equal sides of a triangle , bisects the third side . 2. The bisectors of the ... bisect each of the angles through which it passes , the two diagonals are at right angles to each other . T. E. ...
... bisecting the angle contained by two equal sides of a triangle , bisects the third side . 2. The bisectors of the ... bisect each of the angles through which it passes , the two diagonals are at right angles to each other . T. E. ...
Página 34
... bisect it . CONSTRUCTION . On AB construct an equilateral triangle ABC , and bisect the angle ACB by the straight line CD , meeting AB at D : then AB is bisected as required at D. ( Prop . 1. ) ( Prop . 9. ) A D B PROOF . Because in the ...
... bisect it . CONSTRUCTION . On AB construct an equilateral triangle ABC , and bisect the angle ACB by the straight line CD , meeting AB at D : then AB is bisected as required at D. ( Prop . 1. ) ( Prop . 9. ) A D B PROOF . Because in the ...
Otras ediciones - Ver todas
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Página 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...
Página 420 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Página 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.