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 the same straight line AB , not coinciding ... similar to the segment ADB , and that similar segments of circles con- tain equal angles , the angle ACB is equal to ...
... similar segments of circles , viz . ACB , ADB , be upon the same side of the same straight line AB , not coinciding ... similar to the segment ADB , and that similar segments of circles con- tain equal angles , the angle ACB is equal to ...
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 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.