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 sider |
Inni boken
Resultat 1-5 av 82
Side 7
... given finite straight line . Let AB be the given straight line . It is required to describe an equilateral triangle upon AB . с D Α RE From the center A , at the distance AB , describe the circle BCD ; ( post . 3. ) from the center B ...
... given finite straight line . Let AB be the given straight line . It is required to describe an equilateral triangle upon AB . с D Α RE From the center A , at the distance AB , describe the circle BCD ; ( post . 3. ) from the center B ...
Side 8
... circle CGH , therefore BC is equal to BG ; ( def . 15. ) and because D is the center of the circle GKL , therefore ... given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done ...
... circle CGH , therefore BC is equal to BG ; ( def . 15. ) and because D is the center of the circle GKL , therefore ... given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done ...
Side 45
... given in position and magnitude , a circle may be described from either extremity of the line as a center , and with a radius equal to the length of the line , as in Euc . 1 , 1. It does not admit the description of a circle with any ...
... given in position and magnitude , a circle may be described from either extremity of the line as a center , and with a radius equal to the length of the line , as in Euc . 1 , 1. It does not admit the description of a circle with any ...
Side 51
... circle is employed as a me- chanical instrument , in the same manner as the straight line , and the use made of it ... given line , that two equilateral triangles may be formed on the given line . Prop . II . When the given point is ...
... circle is employed as a me- chanical instrument , in the same manner as the straight line , and the use made of it ... given line , that two equilateral triangles may be formed on the given line . Prop . II . When the given point is ...
Side 66
... radius equal to its distance from one of the given points , will pass through the other point , and the perpendicular will be the locus of all the circles which can be described passing through the two given points . Again , if a third ...
... radius equal to its distance from one of the given points , will pass through the other point , and the perpendicular will be the locus of all the circles which can be described passing through the two given points . Again , if a third ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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.
Side 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.
Side 26 - ... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another.
Side 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.
Side 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.
Side 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...
Side 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.
Side 67 - A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions.