Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Elements of Plane and Spherical Trigonometry |
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Side 63
If a straight line drawn through the centre of a circle bisect a straight line in the circle , which does not pass through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it .
If a straight line drawn through the centre of a circle bisect a straight line in the circle , which does not pass through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it .
Side 64
bisecting AB , which does not pass through the centre , cuts AB at right angles . Again , let CD cut AB at right angles ; CD also bisects AB , that is , AF is equal to FB . The same construction being made , because the radii EA ...
bisecting AB , which does not pass through the centre , cuts AB at right angles . Again , let CD cut AB at right angles ; CD also bisects AB , that is , AF is equal to FB . The same construction being made , because the radii EA ...
Side 68
Therefore one circumference of a circle cannot cut F another in more than two points . PROP . XI . THEOR . 1 If two circles touch each other internally , the straight line which joins their centres being produced , will pass through the ...
Therefore one circumference of a circle cannot cut F another in more than two points . PROP . XI . THEOR . 1 If two circles touch each other internally , the straight line which joins their centres being produced , will pass through the ...
Side 69
If two circles touch each other externally , the straight line which joins their centres will pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point A ; and let F be the centre of ...
If two circles touch each other externally , the straight line which joins their centres will pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point A ; and let F be the centre of ...
Side 70
but it does not pass through it , because the points B , D are without the straight line GH , which is absurd : therefore one circle cannot touch another in the inside in more points than one . Nor can two circles touch one another on ...
but it does not pass through it , because the points B , D are without the straight line GH , which is absurd : therefore one circle cannot touch another in the inside in more points than one . Nor can two circles touch one another on ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1836 |
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |
Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Uten tilgangsbegrensning - 1837 |
Vanlige uttrykk og setninger
ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circle ABC circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremity fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole
Populære avsnitt
Side 53 - 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.
Side 18 - If two triangles have two sides of the one equal to two sides of the...
Side 54 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Side 82 - 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 31 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Side 11 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 21 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Side 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Side 298 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Bibliografisk informasjon
| Tittel | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Elements of Plane and Spherical Trigonometry |
| Forfatter | John Playfair |
| Utgiver | W. E. Dean, 1847 |
| Original fra | University of Michigan |
| Digitalisert | 20. sep 2007 |
| Lengde | 317 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |