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 10
Quadrilateral , by four straight lines . 18. Multilateral figures , or polygons , by more than four straight lines . 19. Of three sided figures , an equilateral triangle is that which has three equal sides . 20. An isosceles triangle is ...
Quadrilateral , by four straight lines . 18. Multilateral figures , or polygons , by more than four straight lines . 19. Of three sided figures , an equilateral triangle is that which has three equal sides . 20. An isosceles triangle is ...
Side 11
All other four sided figures besides these , are called trapeziums . 30. Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . 1.
All other four sided figures besides these , are called trapeziums . 30. Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . 1.
Side 17
By the same construction , each of the halves BAF , CAF , may be divided into two equal parts ; and thus , by successive subdivisions , a given angle may be divided into four equal parts , into eight , into sixteen , and so on . PROP .
By the same construction , each of the halves BAF , CAF , may be divided into two equal parts ; and thus , by successive subdivisions , a given angle may be divided into four equal parts , into eight , into sixteen , and so on . PROP .
Side 20
And hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . XVI . THEOR . If one side of a triangle be . produced , the exterior angle is greater than either of ...
And hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . XVI . THEOR . If one side of a triangle be . produced , the exterior angle is greater than either of ...
Side 28
Neither do they meet on the other side of EF ; for the angles LGH , GHD would then be two angles of a triangle , and less than two right angles ; but this is impossible ; for the four angles KGH , HGL , CHG , GHD are together equal to ...
Neither do they meet on the other side of EF ; for the angles LGH , GHD would then be two angles of a triangle , and less than two right angles ; but this is impossible ; for the four angles KGH , HGL , CHG , GHD are together equal to ...
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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 - 1842 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1840 |
Vanlige uttrykk og setninger
ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circle ABC circumference coincide common consequently construction 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 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 remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole
Populære avsnitt
Side 51 - 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 12 - AB; but things which are equal to the same are equal to one another...
Side 80 - 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 288 - 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.
Side 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line which touches the circle, shall be equal to the angles in the alternate segments of the circle.
Side 52 - 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.
Side 127 - 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.
Side 23 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Side 19 - 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 are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
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, 1837 |
| Original fra | Harvard University |
| Digitalisert | 30. jan 2008 |
| Lengde | 318 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |