The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |
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Página 48
... shew that there may , according to circumstances , be two solutions , one , or none . 7. Describe a circle which shall pass through two given points , and have its centre in a given line . 8. From two given points on the same side of ...
... shew that there may , according to circumstances , be two solutions , one , or none . 7. Describe a circle which shall pass through two given points , and have its centre in a given line . 8. From two given points on the same side of ...
Página 49
... shew that DF , BF , ( drawn to a point F within the triangle ABC but not from the extremities of the base ) are together greater than AC , BC . 11. The difference of any two sides of a triangle is less than the third side . 12. Let AB ...
... shew that DF , BF , ( drawn to a point F within the triangle ABC but not from the extremities of the base ) are together greater than AC , BC . 11. The difference of any two sides of a triangle is less than the third side . 12. Let AB ...
Página 50
... shew that the space included in the second fold is three times that in the first . 31. The quadrilateral figure , whose diameters bisect each other , is a parallelogram . 32. Draw a line which would , if produced , bisect the angle ...
... shew that the space included in the second fold is three times that in the first . 31. The quadrilateral figure , whose diameters bisect each other , is a parallelogram . 32. Draw a line which would , if produced , bisect the angle ...
Página 51
... shew that , according as A and B lie on the same or opposite sides of the line , CF is equal to the semi - sum or semidifference of AD and BE . 36. Through a given point draw a line , such that the parts intercepted by it and two given ...
... shew that , according as A and B lie on the same or opposite sides of the line , CF is equal to the semi - sum or semidifference of AD and BE . 36. Through a given point draw a line , such that the parts intercepted by it and two given ...
Página 52
... shew that DF , EF are in one line . 44. Trisect a right angle . 45. One of the acute angles of a right - angled triangle is three times as great as the other : trisect the smaller of these . 46. If the base of an isosceles triangle be ...
... shew that DF , EF are in one line . 44. Trisect a right angle . 45. One of the acute angles of a right - angled triangle is three times as great as the other : trisect the smaller of these . 46. If the base of an isosceles triangle be ...
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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD angle ABC angle ACB angle BAC base base BC BC is equal bisected centre chord circle circle ABC circumference common described diameter difference divided double draw drawn equal angles equiangular equimultiples extremities fall figure fore four fourth given circle given line given point given straight line greater half inscribed intersection join less Let ABC lines be drawn lines drawn magnitudes manner meet multiple opposite sides parallel parallelogram pass perpendicular plane polygon PROB produced PROP proportionals Q.E.D. PROP ratio rectangle rectangle contained rectilineal figure right angles segment semicircle shew shewn sides similar square square of AC Take taken THEOR third touches the circle triangle ABC Wherefore whole
Pasajes populares
Página 42 - 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.
Página 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 33 - F, which is the common vertex of the triangles: that is », together with four right angles. 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 62 - 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.
Página 22 - If from the ends of a 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.
Página 58 - 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 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.
Página 194 - 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.
Página 2 - 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 : 16.
Página 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Información bibliográfica
| Título | The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso |
| Autor | Euclides |
| Editor | John William Colenso (bp. of Natal) |
| Publicado | 1846 |
| Procedencia del original | Universidad de Oxford |
| Digitalizado | 10 Oct. 2006 |
| Exportar cita | BiBTeX EndNote RefMan |