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 75
... chord of the greater circle , between the extremity of the diameter and the point of section of the perpendicular , will be double of the square of the corresponding chord of the lesser circle . 15. Divide a line in two points equally ...
... chord of the greater circle , between the extremity of the diameter and the point of section of the perpendicular , will be double of the square of the corresponding chord of the lesser circle . 15. Divide a line in two points equally ...
Page 76
... other point in AD : shew that the squares of AF , BF , CF , DF , are together greater than the squares of AE , BE , CE , DE , by four times the square of EF , 24. If from the extremities of any chord in a 76 PROBLEMS .
... other point in AD : shew that the squares of AF , BF , CF , DF , are together greater than the squares of AE , BE , CE , DE , by four times the square of EF , 24. If from the extremities of any chord in a 76 PROBLEMS .
Page 77
... chord in a circle lines be drawn to any point in the diameter to which it is parallel , the sum of their squares is equal to the sum of the squares upon the segments of the diameter . 25. If the sides of a triangle be as 2 , 4 , 5 ...
... chord in a circle lines be drawn to any point in the diameter to which it is parallel , the sum of their squares is equal to the sum of the squares upon the segments of the diameter . 25. If the sides of a triangle be as 2 , 4 , 5 ...
Page 118
... chord PAQ cuts the diameter of a circle in A in an angle which is half a right angle : shew that the squares of AP and AQ are together double of the square of the radius . 6. If two chords intersect in a circle , the difference of their ...
... chord PAQ cuts the diameter of a circle in A in an angle which is half a right angle : shew that the squares of AP and AQ are together double of the square of the radius . 6. If two chords intersect in a circle , the difference of their ...
Page 119
... chord . 16. Of all lines which touch the interior and are bounded by the exterior of two circles which touch internally , the greatest is that which is parallel to the common tangent . 17. Shew that the two tangents to a circle drawn ...
... chord . 16. Of all lines which touch the interior and are bounded by the exterior of two circles which touch internally , the greatest is that which is parallel to the common tangent . 17. Shew that the two tangents to a circle drawn ...
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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 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
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.
Bibliographic information
| Title | 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 |
| Author | Euclides |
| Editor | John William Colenso (bp. of Natal) |
| Published | 1846 |
| Original from | Oxford University |
| Digitized | 10 Oct 2006 |
| Export Citation | BiBTeX EndNote RefMan |