Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes; a Series of Questions on Each Book; and a Selection of Geometrical Exercises from the Senate-house and College Examination Papers, with Hints, &c. Designed for the Use of the Junior Classes in Public and Private Schools. the first six books, and the portions of the eleventh and twelfth books read at CambridgeLongman, Green, Longman, Roberts, and Green, 1868 - 410 páginas |
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Página 139
... inscribed in a circle , are together equal to two right angles . Let ABCD be a quadrilateral figure in the circle ABCD . Then any two of its opposite angles shall together be equal to two right angles . D B Join AC , BD . And because ...
... inscribed in a circle , are together equal to two right angles . Let ABCD be a quadrilateral figure in the circle ABCD . Then any two of its opposite angles shall together be equal to two right angles . D B Join AC , BD . And because ...
Página 156
... inscribed figure be produced , the exterior angle is equal to the opposite angle of the figure . Prop . XXIII . It is obvious from this proposition that of two circular segments upon the same base , the larger is that which contains the ...
... inscribed figure be produced , the exterior angle is equal to the opposite angle of the figure . Prop . XXIII . It is obvious from this proposition that of two circular segments upon the same base , the larger is that which contains the ...
Página 158
... inscribed in a circle ? Are there any analogous conditions requisite that a parallelogram may be described about a circle ? 33 . Define the angle in a segment of a circle , and the angle on a seg- ment ; and shew that in the same circle ...
... inscribed in a circle ? Are there any analogous conditions requisite that a parallelogram may be described about a circle ? 33 . Define the angle in a segment of a circle , and the angle on a seg- ment ; and shew that in the same circle ...
Página 165
... inscribed between them , lie in two lines at right angles to each other . 33. Draw two tangents to a given circle , which shall contain an angle equal to a given rectilineal angle . 34. Describe a circle with a given radius touching a ...
... inscribed between them , lie in two lines at right angles to each other . 33. Draw two tangents to a given circle , which shall contain an angle equal to a given rectilineal angle . 34. Describe a circle with a given radius touching a ...
Página 172
... inscribed in a circle from their middle points intersect in a fixed point . 137. The lines bisecting any angle of a quadrilateral figure in- scribed in a circle , and the opposite exterior angle , meet in the cir- cumference of the ...
... inscribed in a circle from their middle points intersect in a fixed point . 137. The lines bisecting any angle of a quadrilateral figure in- scribed in a circle , and the opposite exterior angle , meet in the cir- cumference of the ...
Términos y frases comunes
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc base BC chord circle ABC constr demonstrated describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid exterior angle Geometrical given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane polygon problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral figure radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles solid angle square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Pasajes populares
Página 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 118 - 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.
Página 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 317 - 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 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Página 88 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 30 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 9 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Página 22 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other...
Página 92 - 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. Let the straight line AB be divided into two equal parts...