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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Page 49
... given one side , an adjacent angle , and the sum or difference of the other two sides . 15. The centre of a circle being given , find two opposite points in the circumference by means of a pair of compasses only . 16. From a given point ...
... given one side , an adjacent angle , and the sum or difference of the other two sides . 15. The centre of a circle being given , find two opposite points in the circumference by means of a pair of compasses only . 16. From a given point ...
Page 75
... given line so that the rectangle of the whole line produced and the original line shall be equal to a given square . 14. If on the radius of a circle a semicircle be de- scribed , and a perpendicular to the common diameter be drawn ...
... given line so that the rectangle of the whole line produced and the original line shall be equal to a given square . 14. If on the radius of a circle a semicircle be de- scribed , and a perpendicular to the common diameter be drawn ...
Page 79
... given line into two parts , so that their rectangle may be equal to a given square . 49. If the areas of a triangle ... circle be described , shew that for every point P in this circle , PA2 + PB2 + PC2 + PD2 is constant , and equals EA2 ...
... given line into two parts , so that their rectangle may be equal to a given square . 49. If the areas of a triangle ... circle be described , shew that for every point P in this circle , PA2 + PB2 + PC2 + PD2 is constant , and equals EA2 ...
Page 81
... given circle . Let ABC be the given circle : it is required to find its centre . Draw within it any straight line AB and bisect it in D ; from the point D draw DC at right angles to AB , and produce CD to E , and bisect CE in F : the ...
... given circle . Let ABC be the given circle : it is required to find its centre . Draw within it any straight line AB and bisect it in D ; from the point D draw DC at right angles to AB , and produce CD to E , and bisect CE in F : the ...
Page 88
... circumference , the least is that between the point without the circle and the diameter , and of the rest , that which is nearer to the least is less than one more remote : and only two equal straight lines can be drawn from the given ...
... circumference , the least is that between the point without the circle and the diameter , and of the rest , that which is nearer to the least is less than one more remote : and only two equal straight lines can be drawn from the given ...
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The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides No preview available - 2016 |
Common terms and phrases
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
Popular passages
Page 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.
Page 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.