Euclid's Elements of Geometry, Libros 1-6;Libro 11Henry Martyn Taylor The University Press, 1895 - 657 páginas |
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Página 11
... triangle . A closed rectilineal figure , which has four sides , is called a quadrilateral A closed rectilineal ... right angle , is called right - angled . The side opposite to the right angle is called the hypo- tenuse § . * A figure ...
... triangle . A closed rectilineal figure , which has four sides , is called a quadrilateral A closed rectilineal ... right angle , is called right - angled . The side opposite to the right angle is called the hypo- tenuse § . * A figure ...
Página 12
... angled . A triangle , which has three acute angles , is called acute- angled . DEFINITION 17. A quadrilateral ... right angle , is called a rectangle . It will be proved later that each angle of a rectangle is a right angle . DEFINITION ...
... angled . A triangle , which has three acute angles , is called acute- angled . DEFINITION 17. A quadrilateral ... right angle , is called a rectangle . It will be proved later that each angle of a rectangle is a right angle . DEFINITION ...
Página 43
... right angles ; ( Constr . ) therefore the sum of the angles DBA , ABC is equal to two right angles . Wherefore , the ... angled triangles have their hypotenuses equal and two other angles equal , the triangles are equal in all respects ...
... right angles ; ( Constr . ) therefore the sum of the angles DBA , ABC is equal to two right angles . Wherefore , the ... angled triangles have their hypotenuses equal and two other angles equal , the triangles are equal in all respects ...
Página 49
... triangle to any point in the opposite side BC between B and C that the angles ABC , BCA are together less than two right ... angled triangles , which have their hypotenuses equal and one side equal to one side , are equal in all respects . 4 ...
... triangle to any point in the opposite side BC between B and C that the angles ABC , BCA are together less than two right ... angled triangles , which have their hypotenuses equal and one side equal to one side , are equal in all respects . 4 ...
Página 55
... right - angled triangle is greater than either of the other sides . 2. The base of a triangle is divided into two parts by the perpen- dicular from the opposite vertex : prove that each part of the base is less than the adjacent side of ...
... right - angled triangle is greater than either of the other sides . 2. The base of a triangle is divided into two parts by the perpen- dicular from the opposite vertex : prove that each part of the base is less than the adjacent side of ...
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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.