Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Appendix by Thos. Kirkland. the first six booksA. Miller & Company, 1876 - 403 Seiten |
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Seite 190
... regular figures in and about circles . Euclid has not given any instance of the inscription or circumscription of rectilineal figures in and about other rectilineal figures . Any rectilineal figure , of five sides and angles , is called ...
... regular figures in and about circles . Euclid has not given any instance of the inscription or circumscription of rectilineal figures in and about other rectilineal figures . Any rectilineal figure , of five sides and angles , is called ...
Seite 192
... regular hexagon and pentagon . The centers of the inscribed and circumscribed circles of any regular polygon are coincident . Besides the circunscription and inscription of triangles and regular polygons about and in circles , some very ...
... regular hexagon and pentagon . The centers of the inscribed and circumscribed circles of any regular polygon are coincident . Besides the circunscription and inscription of triangles and regular polygons about and in circles , some very ...
Seite 193
... regular figures besides these three , can be made to fill up the space round a point ; for any multiple of the interior angles of any other regular polygon , will be found to be in excess above , or in defect from four right angles ...
... regular figures besides these three , can be made to fill up the space round a point ; for any multiple of the interior angles of any other regular polygon , will be found to be in excess above , or in defect from four right angles ...
Seite 194
... regular figures may be inscribed in a circle by the help of Euc . IV . 10 ? 22. What is Euclid's definition of a regular pentagon ? Would the stellated figure , which is formed by joining the alternate angles of a regular pentagon , as ...
... regular figures may be inscribed in a circle by the help of Euc . IV . 10 ? 22. What is Euclid's definition of a regular pentagon ? Would the stellated figure , which is formed by joining the alternate angles of a regular pentagon , as ...
Seite 195
... regular hexagon also a parallelogram ? Would the same observation apply to all regular figures with an even number of sides ? 27. Why has Euclid not shewn how to inscribe an equilateral triangle in a circle , before he requires the use ...
... regular hexagon also a parallelogram ? Would the same observation apply to all regular figures with an even number of sides ? 27. Why has Euclid not shewn how to inscribe an equilateral triangle in a circle , before he requires the use ...
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A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC angle equal Apply Euc base BC chord circle ABC constr describe a circle diagonals diameter divided 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 produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral 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 triangle ABC twice the rectangle vertex vertical angle wherefore
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Seite 93 - If a straight line be bisected and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double of the square on half the line bisected, and of the square on the line made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D ; The squares on AD and DB shall be together double of the squares on AC and CD. CONSTRUCTION. — From the point C draw CE at right angles to AB, and make it equal...
Seite 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.
Seite 145 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Seite 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 on the line between the points of section, is equal to the square on half the line.
Seite 26 - ... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another.
Seite 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 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.
Seite 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...
Seite xv - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Seite 67 - A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions.