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
Página 2
... lines that contain the angle meet one another , is put between the other two letters , and one of these two is ... drawn from a certain point within the figure to the circumference , are equal to one another : XVI . And this point ...
... lines that contain the angle meet one another , is put between the other two letters , and one of these two is ... drawn from a certain point within the figure to the circumference , are equal to one another : XVI . And this point ...
Página 3
... line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a dia- meter and the part of the circumference it cut off . XIX . A segment of a circle is the figure ...
... line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a dia- meter and the part of the circumference it cut off . XIX . A segment of a circle is the figure ...
Página 4
... lines are such as are in the same plane , and , being produced ever so far both ways , do not meet . Let it be granted , POSTULATES . 1. That a straight line may be drawn from any one point to any other point : 11. That a terminated ...
... lines are such as are in the same plane , and , being produced ever so far both ways , do not meet . Let it be granted , POSTULATES . 1. That a straight line may be drawn from any one point to any other point : 11. That a terminated ...
Página 7
... drawn equal to the given straight line BC . Q. E.F. PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater : it ...
... drawn equal to the given straight line BC . Q. E.F. PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater : it ...
Página 15
... line AB , CF has been drawn at right angles to AB . Q. E. F. COR . By the help of this problem , it may be demon- strated that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD ...
... line AB , CF has been drawn at right angles to AB . Q. E. F. COR . By the help of this problem , it may be demon- strated that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD ...
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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
AB is equal ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP quadrilateral rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c THEOR touches the circle triangle ABC twice the rectangle Wherefore
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.