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 1
... magnitude . 11. A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its extreme points . v . A superficies is that which hath only length and breadth ...
... magnitude . 11. A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its extreme points . v . A superficies is that which hath only length and breadth ...
Página 5
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . x . Two straight lines cannot enclose a space . XI . All right angles are ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . x . Two straight lines cannot enclose a space . XI . All right angles are ...
Página 119
... magnitude , touching it and one another ? 12. Describe a circle which shall pass through a given point , and touch a given circle in a given point , the two points not being in a tangent to the given circle . 13. Describe a circle which ...
... magnitude , touching it and one another ? 12. Describe a circle which shall pass through a given point , and touch a given circle in a given point , the two points not being in a tangent to the given circle . 13. Describe a circle which ...
Página 152
... and hence if ABCP , A'B'C'P ' be concentric circles , and ABC , A'B'C ' equi- lateral triangles inscribed in them , shew that AP'2 + BP'2 + CPA'P2 + B ́P2 + C'P2 . BOOK V. DEFINITIONS . I. A LESS magnitude is said 152 PROBLEMS .
... and hence if ABCP , A'B'C'P ' be concentric circles , and ABC , A'B'C ' equi- lateral triangles inscribed in them , shew that AP'2 + BP'2 + CPA'P2 + B ́P2 + C'P2 . BOOK V. DEFINITIONS . I. A LESS magnitude is said 152 PROBLEMS .
Página 153
... magnitudes of the same kind to one another in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . v . The first of four magnitudes is said to have ...
... magnitudes of the same kind to one another in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . v . The first of four magnitudes is said to have ...
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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 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 rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB 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.