Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 páginas |
Dentro del libro
Resultados 1-5 de 54
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 . A D C B Join AC , BD . And ...
... 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 . A D C B Join AC , BD . And ...
Página 156
... inscribed figure be produced , the exterior angle is equal to the opposite angle of the figure . Prop . xx . 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 . xx . 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 ...
Otras ediciones - Ver todas
Términos y frases comunes
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Pasajes populares
Página 54 - If two triangles have two sides of the one equal to two sides of the...
Página 89 - 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 38 - Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Página 144 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 18 - Any two angles of a triangle are together less than two right angles.
Página 266 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 152 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 7 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line; it is required to draw from the point A a straight line equal to BC.
Página 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 96 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...