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 81
... Similar segments of circles are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle : it is required to find its centre . Draw within ...
... Similar segments of circles are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle : it is required to find its centre . Draw within ...
Page 102
... similar segments of circles , viz . ACB , ADB , be upon the same side of D the same straight line AB , not ... similar to the segment ADB , and that similar segments of circles contain equal angles , the angle ACB is equal to the angle ...
... similar segments of circles , viz . ACB , ADB , be upon the same side of D the same straight line AB , not ... similar to the segment ADB , and that similar segments of circles contain equal angles , the angle ACB is equal to the angle ...
Page 103
... similar segments ACB , ADB , upon the same side of the same straight line , AB , cannot but coincide . Wherefore , Upon the same & c . Q.E.D. PROP . XXIV . THEOR . Similar segments of circles upon equal straight lines are equal to one ...
... similar segments ACB , ADB , upon the same side of the same straight line , AB , cannot but coincide . Wherefore , Upon the same & c . Q.E.D. PROP . XXIV . THEOR . Similar segments of circles upon equal straight lines are equal to one ...
Page 105
... similar to the segment EDF , and they are upon equal straight lines BC , EF : But similar segments of circles upon equal straight lines are equal to one another ( 3. 24 ) ; therefore the segment BAC is equal to the segment EDF : But the ...
... similar to the segment EDF , and they are upon equal straight lines BC , EF : But similar segments of circles upon equal straight lines are equal to one another ( 3. 24 ) ; therefore the segment BAC is equal to the segment EDF : But the ...
Page 126
... similar segments of circles be described , and from the extremities of the base tangents to the segment upon it be drawn to cut the other circumferences , the points of intersection and the vertex will be in the same line parallel to ...
... similar segments of circles be described , and from the extremities of the base tangents to the segment upon it be drawn to cut the other circumferences , the points of intersection and the vertex will be in the same line parallel to ...
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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 |