Euclid's Elements of geometry, the first four books, by R. Potts. Corrected and improved1864 |
Dentro del libro
Resultados 1-5 de 32
Página 153
... chord is the straight line joining the extremities of an arc . Every chord except a diameter divides a circle into two unequal segments , one greater than , and the other less than a semicircle . And in the same manner , two radii drawn ...
... chord is the straight line joining the extremities of an arc . Every chord except a diameter divides a circle into two unequal segments , one greater than , and the other less than a semicircle . And in the same manner , two radii drawn ...
Página 156
... chords to the given arc , bisecting them , and from the points of bisection drawing perpendiculars . The point in which they meet will be the center of the circle . This problem is equi- valent to that of finding a point equally distant ...
... chords to the given arc , bisecting them , and from the points of bisection drawing perpendiculars . The point in which they meet will be the center of the circle . This problem is equi- valent to that of finding a point equally distant ...
Página 157
... chord , secant . 2. How does a sector differ in form from a segment of a circle ? Are they in any case coincident ? 3. What is Euclid's criterion of the equality of two circles ? What is meant by a given circle ? How many points are ...
... chord , secant . 2. How does a sector differ in form from a segment of a circle ? Are they in any case coincident ? 3. What is Euclid's criterion of the equality of two circles ? What is meant by a given circle ? How many points are ...
Página 158
... chord of an arc be twelve inches long , and be divided into two segments of eight and four inches by another chord : what is the length of the latter chord , if one of its segments be two inches ? 20. What is the radius of that circle ...
... chord of an arc be twelve inches long , and be divided into two segments of eight and four inches by another chord : what is the length of the latter chord , if one of its segments be two inches ? 20. What is the radius of that circle ...
Página 160
... chords of a circle at right angles to each other , prove that the sum of the arcs AC , BD is equal to the sum of the arcs AD , BC . Draw the diameter FGH parallel to AB , and cutting CD in H. D A B E F G H C Then the arcs FDG and FCG ...
... chords of a circle at right angles to each other , prove that the sum of the arcs AC , BD is equal to the sum of the arcs AD , BC . Draw the diameter FGH parallel to AB , and cutting CD in H. D A B E F G H C Then the arcs FDG and FCG ...
Otras ediciones - Ver todas
Euclid's Elements of Geometry, the First Four Books, by R. Potts. Corrected ... Euclides Sin vista previa disponible - 2016 |
Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ... Euclides Sin vista previa disponible - 1864 |
Términos y frases comunes
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal Apply Euc axiom base BC bisecting the angle chord circle ABC circumference construction demonstrated describe a circle diagonals diameter double draw equal angles equal to twice equiangular equilateral triangle Euclid Euclid's Elements exterior angle Geometry given angle given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle Let ABC line AC line CD line joining lines be drawn meet the circumference opposite angles opposite sides parallel parallelogram pentagon perpendicular porism problem produced Prop proved quadrilateral figure radius rectangle contained remaining angle right angles right-angled triangle segment semicircle shew shewn side BC square on AC tangent THEOREM touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Pasajes populares
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 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 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 54 - If two triangles have two sides of the one equal to two sides of the...
Página 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 85 - 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 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...
Página 41 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Página 126 - EF, that is, AF, is greater than BF : Again, because BE is equal to CE, and FE common to the triangles BEF, CEF, the two sides BE, EF are equal to the two CE, EF; but the angle BEF is greater than the angle CEF ; therefore the base BF is greater (24. 1.) than the base FC ; for the same reason, CF is greater than GF. Again, because GF, FE are greater (20.