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 |
Dentro del libro
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Página 49
... difference of any two sides of a triangle is less than the third side . 12. Let AB bisect CD at right angles in B ; from any point E draw EC through the nearest extremity of CD cutting AB in F ; and prove that the difference of EF and ...
... difference of any two sides of a triangle is less than the third side . 12. Let AB bisect CD at right angles in B ; from any point E draw EC through the nearest extremity of CD cutting AB in F ; and prove that the difference of EF and ...
Página 51
... difference of BD and CE . 35. If AB be bisected in C , and from A , B , C parallel lines be drawn cutting a given line in D , E , F , shew that , according as A and B lie on the same or opposite sides of the line , CF is equal to the ...
... difference of BD and CE . 35. If AB be bisected in C , and from A , B , C parallel lines be drawn cutting a given line in D , E , F , shew that , according as A and B lie on the same or opposite sides of the line , CF is equal to the ...
Página 52
... difference of the angles at the base of any triangle is double of the angle between two lines drawn from the vertex , one bisecting the vertical angle and the other perpendicular to the base . 50. In the base BC of an isosceles triangle ...
... difference of the angles at the base of any triangle is double of the angle between two lines drawn from the vertex , one bisecting the vertical angle and the other perpendicular to the base . 50. In the base BC of an isosceles triangle ...
Página 53
... difference between each side and the adjacent segment of the base : construct the triangle . 60. Let AD be drawn perpendicular to the base BC of a triangle , in which the angle B is double of the angle C ; in AB , produced or not ...
... difference between each side and the adjacent segment of the base : construct the triangle . 60. Let AD be drawn perpendicular to the base BC of a triangle , in which the angle B is double of the angle C ; in AB , produced or not ...
Página 54
... difference of the segments of the base , according as the greater angle B is greater or less than a right angle . 62. The lines which bisect the angles of any parallelogram , form a rectangular parallelogram , whose diameters are ...
... difference of the segments of the base , according as the greater angle B is greater or less than a right angle . 62. The lines which bisect the angles of any parallelogram , form a rectangular parallelogram , whose diameters are ...
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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 |